Question

Решите неравенство ||||||х|+3|-1|+2|-3|-2|≤2

Answer 1

$||||||x|+3|-1|+2|-3|-2|\leq2\\-2\leq|||||x|+3|-1|+2|-3|-2\leq2\\0\leq|||||x|+3|-1|+2|-3|\leq4\\-4\leq||||x|+3|-1|+2|-3\leq4\\-1\leq||||x|+3|-1|+2|\leq7\\-7\leq|||x|+3|-1|+2\leq7\\-9\leq|||x|+3|-1|\leq5\\-5\leq||x|+3|-1\leq5\\-4\leq||x|+3|\leq6\\-6\leq|x|+3\leq6\\-9\leq|x|\leq3\\-3\leq x\leq3$

Ответ: $x\in [-3; 3]$